The discussion regarding Berkshire's float and how it is invested inevitably leads to the question of whether the "float based valuation" models that were very popular 10-15 years ago ultimately led investors astray and resulted in valuations for Berkshire that, in retrospect, can be considered above fair value.

The float based valuation model is one developed by Alice Schroeder in the late 1990s and published in a 1999 report which is now available on a number of sites online. I think most everyone here is familiar with the methodology. Although not explicitly endorsed by Warren Buffett, many believe that Schroeder's access to Buffett in the late 1990s combined with the fact that she was subsequently selected as his official biographer indicate Buffett's general agreement with her work and methodology.

Although I used this methodology for years as my primary guide to Berkshire's value, I have come to believe that it is of very limited utility and can lead investors to overpay. The main problem with the model is the very extreme sensitivity of the model's results based on relatively small changes to the input variables used to calculate the present value of Berkshire's float: Investment Returns, Cost of Float, Growth of float, and Discount Rate.

There is often debate regarding whether Berkshire's float serves the functional equivalent of equity. What's interesting is that using the float based valuation model, the present value of Berkshire's float usually far exceeds its nominal value based on only moderate input variables. For example, when I wrote a report on Berkshire two years ago, Berkshire had float of $65.8 billion. I computed the present value of the float to be $125 billion based on input variables of 6% for investment returns, -0.7% for the cost of float, 3% for the growth of float, and 6% for the discount rate. Essentially, I was saying that the present value of Berkshire's float was, at the time, nearly twice the actual dollar amount of float. In retrospect, the rate of return on investments was probably too aggressive as was the growth rate of float. However, you can play with the model and even more conservative estimates result in valuing float quite highly.

To Jim's point, if we assume that float will be invested in fixed income and cash (for whatever reasons), then investment returns must be set at a much lower rate based on the current interest rate environment. Buffett has also told us to not expect any significant growth of float going forward. Although the cost of float is likely to remain negative, that is merely one variable in the float valuation model and not the dominant variable if one assumes significant changes to the growth of float and investment returns.

So where am I going with this? Basically, over the past two years since writing the report (and mostly over the past year or so) I have come to the realization that the float based model may be an intellectually "elegant" model but one of limited utility in practice. The assumptions that must be made and the sensitivity of those assumptions to the valuation of float are just too volatile to be consistently useful over time.

I believe that the two-column method is more appropriate for Berkshire and far less likely to lead to errors. The model is also arguably more appropriate for Berkshire as a greater percentage of the company's value originates from non-insurance operations vs. the composition of the company when Schroeder's model was first developed. Buffett has endorsed this model in shareholder letters. The two-column model DOES assign value to float implicitly based on the fact that investments per share are used as one of the "columns" and a portion of the investments are funded by float. Essentially, this model is saying that float is the functional equivalent of equity which is reasonable as long as the cost of float is negative.

It is important to revisit valuation models and opinions from the past to see how they conform to reality over time. Berkshire's stock price has underperformed my expectations in recent years but that is not why I have in recent years come to question the float based model. That has more to do with the overall model making less sense to me today than it did in the past.

The good news is that the two-column method easily justifies a $165K stock price today. The only way I see this model being invalidated in the years to come is if Berkshire's insurance operations suddenly deteriorate to the point where the cost of float gets to be high thereby invalidating the assumption that float has the functional equivalent of equity for shareholders.

I have come to the realization that the float based model may be an intellectually "elegant" model but one of limited utility in practice. The assumptions that must be made and the sensitivity of those assumptions to the valuation of float are just too volatile to be consistently useful over time.

This is pretty much the exact same reason I never use a discounted cash flow model, too.I can never seem to get any more obviously useful information out of the calculation than what I put into it, and rarely even that much.One of the few times I did it I concluded that BNSF was worth about$190 per share, twice what was paid, and that opinion was not very well received to say the least.http://boards.fool.com/what-was-he-missing-the-attractivenes...It seems a little more plausible now with UNP's stock price at 2.5 timesthe level it was then, perhaps the complaints will tail off andI'll start believing discounted cash flow models. Maybe pigs will fly.

I believe that the two-column method is more appropriate for Berkshire and far less likely to lead to errors. I have gradually some around to this way of thinking too.It's really too simple to be really good, as it doesn't take into account that Berkshireis in large part an insurance company, but on the flip side it doesavoid the pitfalls of some dubious assumptions when valuing insurers.I do a lot of cyclical adjustments and haircuts, but 2-col gives good solid take-it-to-the-bank numbers that don't jump around wildly with your assumptions.

The good news is that the two-column method easily justifies a $165K stock price today.Indeed. You have to work reasonably hard indeed to get figures lower than that.

Like you, I like to look back at my old valuation methodologies andsee whether the results were numbers which I would now consider overvalued.Not too much, it seems; only a little.In late 2007 my first sale due to perceived overvaluation was at 1.706x most recent book.I might start lightening up as low as (say) 1.55x these days, but not lower.So, my valuation attitudes are at most 9% cheaper.Most of that is reduced expectations of the long run average multipleswe'll see Mr Market putting on the firm's operations in future.

In fact next time the price is rising I'll probably use a two column method, and just argue with myself about the size of the haircut for the investments per share and the multiple of pretax earnings to use.e.g., a 15% haircut on investments per share for the value of the long run cyclically adjusted drag from cash and a multiple of 9x cyclicallyadjusted pretax earnings (the average multiple for the average UScompany in the average year) gives me $164.1k from Q3 statements.That's probably pretty conservative.So much work to calculate this all the time—the dang number keeps going up!

In late 2007 my first sale due to perceived overvaluation was at 1.706x most recent book. I might start lightening up as low as (say) 1.55x these days, but not lower.

My main mistake over the past decade was to not lighten up on Berkshire in any meaningful way either at the late 2007 highs or during the early October 2008 rally. I sold nothing at all in late 2007 and only a very small amount in early October 2008.

I believe that the primary reason for the mistake was use of the float based valuation model which, at year end 2007, was estimated at $153K based on my input variables. This was 1.96x year end book value per share. So in late 2007 in my mind we were just approaching fair value.

At 12/31/2007, the two column approach would have yielded much more modest results. Investments and cash per A share was just over $91K. Pre-tax non-insurance earnings were $6.7 billion, or roughly $4,300 per share. Using a 8x multiple would yield an estimate of IV of around $125K and a more reasonable 1.6x book multiple.

It is always difficult to avoid hindsight bias when revisiting investment mistakes from the past but I am pretty much convinced that relying heavily on the float based valuation model at Berkshire's record highs is the most significant investment mistake I've made to date. Fortunately I've been bailed out partially by Berkshire's business performance over the years and, from inception, all of my positions in Berkshire now exceed the returns of the S&P 500 and most by a very substantial margin. That just goes to show that owning a wonderful business can blunt the impact of stupid decisions when it comes to buying and selling the stock of the business.

At 12/31/2007, the two column approach would have yielded much more modest results. Investments and cash per A share was just over $91K. Pre-tax non-insurance earnings were $6.7 billion, or roughly $4,300 per share. Using a 8x multiple would yield an estimate of IV of around $125K and a more reasonable 1.6x book multiple.

One additional point on this: One could argue that Berkshire would have been overvalued even at $125K in late 2007. However, I am not sure that this argument would be possible without having benefit of the knowledge of subsequent events - specifically the economic recession of the subsequent two years.

I would not beat myself up over having made a decision to hold Berkshire at $120K or $125K in late 2007 because I would not have had the benefit of future knowledge required to consider the shares overvalued at that point. Yes, it would have been better to sell even at $125K in late 2007 but that gets into the realm of acting on skills more related to economic forecasting and market timing than an assessment of intrinsic value of the business itself.

The more intelligent way of looking at Berkshire which I follow religiously today is simple: Try to be conservative with estimates of intrinsic value for Berkshire. Compare the degree of undervaluation of Berkshire vs. other opportunities that I know of and have similar conviction in. Be willing to sell Berkshire shares even at low valuations if I strongly believe that something else is a better risk/reward scenario at prevailing prices. And finally and most importantly, do not hesitate to reduce my allocation to Berkshire to levels more resembling a "normal" position size the next time it approaches intrinsic value since I do not consider 8-10% annualized returns (Berkshire's likely IV growth) to be an acceptable rate of return for an over-sized portion of my portfolio.

And also, do not let the tax tail wag the investment dog - as Munger might say, "suck it up and cope" if intelligent investing requires payment of capital gains taxes on (hopefully rare) occasions.

My main mistake over the past decade was to not lighten up on Berkshire in any meaningful way either at the late 2007 highs or during the early October 2008 rally. I sold nothing at all in late 2007 and only a very small amount in early October 2008.

I believe that the primary reason for the mistake was use of the float based valuation model which, at year end 2007, was estimated at $153K based on my input variables. This was 1.96x year end book value per share. So in late 2007 in my mind we were just approaching fair value.

At 12/31/2007, the two column approach would have yielded much more modest results. Investments and cash per A share was just over $91K. Pre-tax non-insurance earnings were $6.7 billion, or roughly $4,300 per share. Using a 8x multiple would yield an estimate of IV of around $125K and a more reasonable 1.6x book multiple.

It is always difficult to avoid hindsight bias when revisiting investment mistakes from the past but...

I sold about a third of my Berkshire shares around $135,000 per A share, and that has obviously worked out well. But the flip side of selling a small amount when it's overpriced is that you are probably going to buy it back when it slips back into fair value, so you can't reasonably have expected to sell at $135k and buy back at the nadir, which turned out to be $73k. More realistically, you would have done like me and bought back most of those shares at a somewhat lower price, in my case around $120k. (I have also bought more shares at lower prices.)

The other point about pricing exit points from this holding is that, while a sale at $145k would have been a great move in retrospect, it might be dangerous to over-tune the valuation parameters to produce a selling price based on that recent example. While being conservative in valuation seems like a conservative idea, it is the reverse if it gets you out of a conservative investment at a price that is too low! In your example of a 2-column calculation, not only do you not give any credit to Berkshire's businesses as being better than average, you actually penalize them, with an 8x pre-tax multiple, and make no allowance for the average underwriting gains. A more neutral valuation would be to take a 9x multiple, with $1000 in underwriting gains (still lower than the 10-year average), which would give you $91k +9*5,300 = $139k. Yes, shares slipped over this level for a few weeks, but only just. And yes, your lower level o $125k would have worked better last time around, but if that level gets you out this time, it may well be that you find yourself having fought the previous war and losing the current one, if valuation levels rise to higher multiples that were more typical in the past.

Looking back at the thread, I see you have already posted again and I agree with your similar point about not beating oneself up about an investment decision that only looks obvious in hindsight. At investments + 8 or 9 or 10 times pre-tax earnings, with or without underwriting gains, 2007 and 2008 levels only just represented full value, and we have lots of room at current prices before we have to start worrying about which numbers to use.